(4x+2)*(2x+3)=30

Solution for (4x+2)*(2x+3)=30 equation:

(4x+2)(2x+3)=30

We move all terms to the left:

(4x+2)(2x+3)-(30)=0

We multiply parentheses ..

(+8x^2+12x+4x+6)-30=0

We get rid of parentheses

8x^2+12x+4x+6-30=0

We add all the numbers together, and all the variables

8x^2+16x-24=0

a = 8; b = 16; c = -24;
Δ = b2-4ac
Δ = 162-4·8·(-24)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-32}{2*8}=\frac{-48}{16}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+32}{2*8}=\frac{16}{16}
=1
$